In this recent question Math puzzles for dinner we had a nice time as we were asked to provide new maths puzzles for dinners. I suggested the following:

Given three equal sticks, and some
thread, is it possible to make a rigid
object in such a way that the three
sticks do not touch each other? (all
objects are 1 dimensional; sticks are
straight and rigid, and the thread is
inestensible).

I'm not particularly fond of maths puzzles, and I found this one in order to satisfy the party in a dinner of non-mathematic people, when I'm asked for a puzzle. Indeed, it's suitable for a dinner, and people get to the right conclusion in reasonable time, amusing themselves and disputing a bit.

Possibly as a consequence of the fact that I always proposed it to non-mathematicians, who are not interested in the proof, now I realized that I do not have, or I forget, the proof for the answer (a bit embarassing indeed). Can somebody find a quick proof for the answer, without too many technical computations?